CCH Powder as the mysterious Oracle also is mysteriously hammy
Name's the Same: The thief that was killed by the Cave of Wonders in the first film was also named Cassim.
What Could Have Been: Mozenrath was originally planned as the villain in the third film. However, whether he would actually be Aladdin's brother is another story - this is fan speculation, not Word of God.
Sean Connery was originally considered for the voice of Cassim.
The Triumphant Reprise of Arabian Nights at the end of this movie was originally meant for the end of the original film when the Peddler was slated to be the narrator, who would appear at certain points to give the audience the scoop on the story so far through various reprises of Arabian Nights. This reprise, in particular, would've been sung as the Peddler packed up all his stuff, hopped onto his camel and went riding into the night, saying goodbye to the audience to mark the end of the legend.